Why am I still up?

Well, I'm happy that I've gotten through the day. Last night I tried to make a promise to myself not to hit snooze, because I needed time to study finance and history of rock music. That didn't happen, so I got up 10 minutes later than planned. Then after my first class (finance), I felt like I'd fall asleep any second, so I ran in to Selleck to get some caffeine + sugar into my blood. Compilers was alright. Powerwalking from Avery to Kauffman to Westbrook in 15 minutes was not fun. I had to do this because I brought 2 pens with me but no pencils, and the rock music test was on a scantron :-(

Design studio class was not horribly boring (just highly boring, instead). Hmm... what else happened... I went over to Abel to eat dinner with Megan, and I went to this math problem solving session. I was one of two people there. The other was an extraordinarily bright high school sophmore from Lincoln East (Alex Churchill) who attended MOSP in the summer.

Now I've got a few interesting problems to work on:

1. find all roots of P_m(x) = x^4 + x^3 + x^2 + mx + m^2


2. Let x_i (i = 1 to n-1) be the roots (except 1) of x^n -1 for n >= 2. Prove that
   1/(1-x_1) + 1/(1-x_2) + ... + 1/(1-x_n) = (n-1)/2


3. Let P be an nth degree polynomial with integer coefficients and at least one integer root. Prove that n! | P(1)P(2)P(3)... P(n)